A stochastic model for evolution of sociality in insects

Area of Science:

• Population Biology
• Evolutionary Biology
• Mathematical Modeling

Background:

• Eusocial insects exhibit complex social structures and altruistic behaviors.
• Understanding the evolution of altruism in these species is a key challenge.
• Worker-brood relatedness is crucial for explaining altruistic traits.

Purpose of the Study:

• To develop a stochastic model for eusocial insect population dynamics.
• To investigate the influence of demographic parameters and queen replacement on worker-brood relatedness.
• To analyze estimators for worker-brood relatedness and their standard errors.

Main Methods:

• Utilized random (matrix) difference equations to model population dynamics.
• Simulated insect colonies with queen replacement events.
• Examined the impact of stochastic variations in survival and other rates.
• Investigated demographic parameters and queen takeover probabilities.

Main Results:

• The model quantifies how random variations in rates affect population dynamics.
• Worker-brood relatedness is shown to be influenced by demographic factors and queen turnover.
• Simulation results provide insights into colony behavior under queen replacement.
• Two estimators for worker-brood relatedness were studied, with procedures for standard error estimation.

Conclusions:

• The stochastic model provides a framework for studying eusocial insect population biology.
• Demographic parameters and queen replacement significantly impact worker-brood relatedness, offering insights into altruism.
• The study offers methods for estimating worker-brood relatedness and constructing confidence intervals.